The argument with the contraceptive pill is interesting. If you are on (a specific type of) pill, the risks of blood clots are a bit higher. If you are overweight and on that pill, chances get higher. If you are older and on that pill (which GP tend to not prescribe so much for women over 40), chances are higher. If you are overweight and older, forget it, they shouldn't prescribe the combined pill.
With Covid, the risks of blood clots are so far only age based. NO other correlation has been established.
When I took the pill, I was explained very clearly what the risks were, repeated every single time I had my prescription renewed, explained what the symptoms were. GP didn't renew prescription when I got to 40 because of increased risks. I was weighed, to check the correlation overweight/increased risks.
Had AZ jab last week and not a peep about the risks of blood clots. I am hoping this has changed already.